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Mathematical aspects of turbulence: where do we stand?

Participation in INI programmes is by invitation only. Anyone wishing to apply to participate in the associated workshop(s) should use the relevant workshop application form.

Programme
4th January 2022 to 24th June 2022
Organisers: 
John Gibbon Imperial College London
Charles R. Doering University of Michigan
Dan Henningson KTH - Royal Institute of Technology
Rich Kerswell University of Cambridge
Anna Laura Mazzucato Pennsylvania State University
Beverley McKeon CALTECH (California Institute of Technology)
Rahul Pandit Indian Institute of Science
Leslie Smith University of Wisconsin-Madison
Edriss Titi University of Cambridge, Texas A&M University, Weizmann Institute of Science
Steven Tobias University of Leeds

Programme theme

Despite the heavy deployment of effort and resources in the study of turbulent fluid flows for well over a century, fundamental questions remain stubbornly unanswered. The associated issues range so widely across the mathematical, physical and engineering sciences that no single research programme can hope to cover all aspects of the subject. This particular programme will concentrate upon the more mathematical concerns, addressing a significant range of topics including:

  1. Analysis of the incompressible Navier-Stokes and Euler equations;
  2. Modelling and analysis of turbulent transport, mixing and scaling processes;
  3. Inhomogeneous and anisotropic wall-bounded flows and transition to turbulence;
  4. Geophysical turbulence including atmospheric, oceanographic and planetary flows.

Recent years have witnessed many analytical and computational advances in our understanding of the structural and dynamical properties of solutions of the incompressible Navier-Stokes and Euler equations and associated models, but many mathematical issues require further investigation. And despite the pressing demand for practical answers, there is nevertheless a need for longer-term thinking about how the most recent developments in mathematical analysis can be leveraged into a wider understanding of physical processes. For example, the regularity and singularity results in the primitive equations of geophysical fluid dynamics can impact climate science models. The introduction of convex integration machinery that has been instrumental in completing the proof of the Onsager conjecture and establishing non-unique weak solutions for the Euler and the Navier-Stokes equations can bring insights into the dissipative anomaly conjecture, a.k.a. Kolmogorov's zero-th law of turbulence. Singularity results for the Euler equations and advances on the Prandtl equations and boundary layer theory relevant to wall-bounded turbulence can have significant engineering applications.

Through a range of events this programme will bring researchers from a broad range of disciplines together to consider these issues. It will provide the space for the type of collaborative interdisciplinary thinking necessary for the formulation of new ideas and research directions.

University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons